We are a local business and would prefer that our customers pay via Electronic Money Transfer, or by cash when their order is picked up or delivered.

Is there a way to have the order processed, ie so we are notified there is an order, without having to go through Paypal or another payment provider? In other words, can the customer submit the order and then make payment as two separate events, rather than being forced to make the payment before the order is submitted?

You would want to use the form builder for something like that.